Inversion of probabilistic models of structures using measured transfer functions

The aim of this thesis is to develop a methodology for the experimental identification of probabilistic models for the dynamical behaviour of structures. The inversion of probabilistic structural models with minimal parameterization, introduced by Soize, from measured transfer functions is in particular considered. It is first shown that the classical methods of estimation from the theory of mathematical statistics, such as the method of maximum likelihood, are not well-adapted to formulate and solve this inverse problem. In particular, numerical difficulties and conceptual problems due to model misspecification are shown to prohibit the application of the classical methods. The inversion of probabilistic structural models is then formulated alternatively as the minimization, with respect to the parameters to be identified, of an objective function measuring a distance between the experimental data and the probabilistic model. Two principles of construction for the definition of this distance are proposed, based on either the loglikelihood function, or the relative entropy. The limitation of the distance to low-order marginal laws is demonstrated to allow to circumvent the aforementioned difficulties. The methodology is applied to examples featuring simulated data and to a civil and environmental engineering case history featuring real experimental data.